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Article Dans Une Revue Numerical Methods for Partial Differential Equations Année : 2013

Convergence analysis of an hp finite element method for singularly perturbed transmission problems in smooth domains

Xenophontos Christos
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Résumé

We consider a two-dimensional singularly perturbed transmission problem with two different diffusion coefficients, in a domain with smooth (analytic) boundary. The solution will contain boundary layers only in the part of the domain where the diffusion coefficient is high and interface layers along the interface. Utilizing existing and newly derived regularity results for the exact solution, we prove the robustness of an hp finite element method for its approximation. Under the assumption of analytic input data, we show that the method converges at an "exponential" rate, provided the mesh and polynomial degree distribution are chosen appropriately. Numerical results illustrating our theoretical findings are also included.

Dates et versions

hal-03212516 , version 1 (29-04-2021)

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Citer

Serge Nicaise, Xenophontos Christos. Convergence analysis of an hp finite element method for singularly perturbed transmission problems in smooth domains. Numerical Methods for Partial Differential Equations, 2013, 29 (6), pp.2107-2132. ⟨10.1002/num.21793⟩. ⟨hal-03212516⟩
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